Herein, a multidimensional image is to be understood to mean, for example, an intensity image formed by points which are pixels arranged in a two-dimensional matrix in space, the intensity of the pixels being a third dimension, or an intensity image formed by points which are voxels arranged in a three-dimensional matrix in space, the intensity of the voxels being a fourth dimension. The segmentation in an image processing method determines segments which are regions of different intensity of the image. The boundaries of the segments are called interfaces.
An image processing method for performing segmentation of an image is already known from the publication "A Multiscale Algorithm for Image Segmentation by Variational Method" by G. Koepfler, C. Lopez, J. M. Morel in "SLAM J. Numer. Anal., Vol. 31, No. 1, pp. 282-299, February 1994". The method described in the cited publication includes the processing of a two-dimensional image which initially comprises regions formed by pixels which are delimited by interfaces and a given number of which has substantially the same intensity. To this end, the method includes a step in which a segmentation algorithm is applied. The proposed algorithm aims to eliminate the largest possible number of interfaces in order to merge adjacent regions whose intensities are practically identical. This algorithm uses a cost function called Energy. The merging of two adjacent regions is possible only in the case in which the Energy function is minimized. This Energy function comprises two terms: a first term which takes into account the intensity variance in each region of the image and a second term which takes into account the total length of the boundaries in the image, weighted by a so-called scale parameter .lambda.. The execution of the algorithm consists first of all in assigning the value 1 to the scale factor .lambda. and in merging two adjacent regions, if any, which minimize the Energy function. The resultant regions are then re-organized by elimination of the interface of the two merged regions, the terms of the Energy function are calculated again and a new attempt for a merger is made, utilizing the scale factor .lambda.=1. This operation is repeated until there is no longer any region having an adjacent region for a merger when the scale factor .lambda.=1. After each merger the resultant regions are re-organized by elimination of the interfaces. Subsequently, the same operations are performed with the scale parameter .lambda.=2, etc., until the Energy function cannot be further minimized. For completion the interfaces of the adjoining regions of different intensity are concretized by way of edges and are plotted in the original image. According to this algorithm, when the term linked to the length of the interfaces has a high cost, there is a tendency to eliminate the interface of the two adjoining regions causing such a high cost, provided that the intensity variance between these regions is small, thus inviting the merging of the two adjoining regions in order to minimize the Energy function. Because the aim is to merge the regions while starting by using the lowest value of the scale parameter .lambda., at first the interfaces are not severely treated, so that numerous adjoining regions having a very similar intensity are allowed to preserve their interface for a long time. Subsequently, as the value of the scale parameter .lambda. increases, the regions are merged two by two in a slow and gradual manner until the Energy function cannot be minimized further. This algorithm holds for several image scales, hence the names scale parameter or pyramidal parameter .lambda..
It is a major problem that the segmentation method known from the cited document is very costly in respect of calculation time, because the regions are merged in a very gradual manner while utilizing first of all the lowest possible value of the parameter .lambda. which is subsequently increased slowly step by step, so that the resultant regions, must be reorganized after each merger, involving a new calculation of the terms of the Energy function, so as to attempt anew the minimization of the Energy function and, occasionally, to execute another merger.
An even more significant problem is that it cannot be ensured that a merger between two adjacent regions which have substantially the same intensity but nevertheless belong to different objects will be avoided.